Bounded Positive Solutions of Quasilinear Schrödinger Equations

Abstract

Quasilinear differential equations (1) are considered in exterior domains , where Δⁿ is the n-dimensional Laplacian and f satisfies non-negativity, continuity, and monotony hypotheses. Necessary and sufficient conditions on f are found for the existence of uniformly positive bounded solutions of (1) in , and corresponding theorems for n≧3. Although the emphasis is on partial differential equations, the conclusions are new even in the case n= 1.

AMS(MOS) 35B35, 35B05

Secondary: 35J10, 35J60, 35A05

University of British Columbia, Vancouver, Canada V6T 1Y4. Support from the Natural Sciences and Engineering Research Council Canada (Grant No. A3105) is acknowledged with gratitude.

University of British Columbia, Vancouver, Canada V6T 1Y4. Support from the Natural Sciences and Engineering Research Council Canada (Grant No. A3105) is acknowledged with gratitude.

Notes

University of British Columbia, Vancouver, Canada V6T 1Y4. Support from the Natural Sciences and Engineering Research Council Canada (Grant No. A3105) is acknowledged with gratitude.

Additional information

Notes on contributors

Robert Gilbert